Effective hydrodynamic boundary conditions for microtextured surfaces

TL;DR

This study measures how microscopic grooves on a surface reduce hydrodynamic drag on a sphere, introducing an effective boundary condition that simplifies complex textured surfaces into an equivalent smooth boundary.

Contribution

The paper introduces an effective no-slip boundary condition at an intermediate plane to accurately model hydrodynamic forces on microtextured surfaces, linking it to geometric parameters.

Findings

Significant reduction in hydrodynamic resistance due to microtexturing.

Effective boundary condition accurately predicts force reduction.

Analytical formula relates effective plane position to surface geometry.

Abstract

We report measurements of the hydrodynamic drag force acting on a smooth sphere falling down under gravity to a plane decorated with microscopic periodic grooves. Both surfaces are lyophilic, so that a liquid (silicone oil) invades the surface texture being in the Wenzel state. A significant decrease in the hydrodynamic resistance force as compared with that predicted for two smooth surfaces is observed. To quantify the effect of roughness we use the effective no-slip boundary condition, which is applied at the imaginary smooth homogeneous isotropic surface located at an intermediate position between top and bottom of grooves. Such an effective condition fully characterizes the force reduction measured with the real surface, and the location of this effective plane is related to geometric parameters of the texture by a simple analytical formula.